微分几何讨论班（2024春第6讲）

题目：New minimal Lagrangian surfaces in CP^2

报告人：Sebastian Heller 教授（BIMSA）

时间：2024年5月15日 15:45-16:45

地点：沙河主E405

摘要：An immersion f : Σ→CP² is called a minimal Lagrangian surface if it is minimal with respect to the Fubini study metric and Lagrangian with respect to the Kähler form. Besides the real projective plane and minimal Lagrangian tori, which can all be constructed via integrable systems methods, the only known compact examples have been obtained by Haskins and Kapouleas for odd genera. In this talk, we explain the construction of new compact minimal Lagrangian surfaces of genus g =(k−2)(k−1)/2 for large k∈N using gauge theoretic and loop group factorization methods. These surfaces are analogous to Lawson’s minimal surfaces in the 3-sphere and coincide with the projective plane and the Clifford torus for k = 2, 3, respectively. We determine their symmetry groups and show that the underlying Riemann surfaces are the Fermat curves. We also discuss further geometric properties such as their area and Willmore energy. This talked is based on joint work with Charles Ouyang and Franz Pedit.

报告人简介：Sebastian Heller, 北京雁栖湖应用数学研究院（BIMSA）教授，博士生导师，曾在德国图宾根大学与海德堡大学工作。研究兴趣包括：调和映照、极小曲面、CMC曲面、模空间的几何与分析、Higgs bundle与Hitchin systems、可积系统，在JDG、Comm. Math. Phys.、Math. Ann.、P. Roy. Soc. A等国际重要期刊发表论文43篇，引用202余次，在国际会议、论坛等做报告21场次。

邀请人：谢振肖